Details

Time bar (total: 26.5s)

sample249.0ms

Algorithm
intervals
Results
66.0ms85×body1280valid
45.0ms10×body160valid
30.0ms255×body80valid
27.0ms50×body640valid
12.0ms31×body320valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.2b
(pow (exp y.im) (atan2 x.im x.re))
1.5b
(* (atan2 x.im x.re) y.re)
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
175×add-sqr-sqrt
173×*-un-lft-identity add-cube-cbrt
153×unpow-prod-down
51×sqr-pow
29×add-exp-log
25×associate-/r*
21×div-exp
11×add-cbrt-cube
9×div-inv
8×pow-to-exp pow-exp
7×pow1 associate-/l*
4×expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow exp-prod associate-*r* associate-*l*
1×cos-sum clear-num frac-2neg pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 286
Calls
4 calls:
29.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
4.0ms
(pow (exp y.im) (atan2 x.im x.re))
8.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series785.0ms

Counts
4 → 12
Calls
4 calls:
480.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
44.0ms
(pow (exp y.im) (atan2 x.im x.re))
26.0ms
(* (atan2 x.im x.re) y.re)
234.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify820.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11409
0529

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize58.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series562.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (atan2 x.im x.re) y.re)
161.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
189.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
188.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts
62 → 62
Iterations
IterNodes
done5000
33485
2528
1154
078

prune780.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize65.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
10.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (atan2 x.im x.re) y.re)
181.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
187.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
210.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts
62 → 62
Iterations
IterNodes
done5000
33485
2528
1154
078

prune867.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize84.0ms

Local error

Found 4 expressions with local error:

32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
32.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 cos-sum *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
209.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
185.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
183.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
52 → 52
Iterations
IterNodes
done5000
31063
2251
195
050

prune768.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

regimes709.0ms

Accuracy

64.9% (1.6b remaining)

Error of 6.2b against oracle of 4.6b and baseline of 9.1b

bsearch7.0ms

simplify9.0ms

Iterations
IterNodes
done46
146
037

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.1s2058×body1280valid
2.1s7977×body80valid
1.4s1493×body640valid
390.0ms653×body320valid
100.0ms301×body160valid